24Exponential Smoothing EquationsFt = Ft-1 + (At-1 - Ft-1)Ft = Forecast valueAt = Actual value = Smoothing constantYou may wish to discuss several points:- this is just a moving average wherein every point in included in the forecast, but the weights of the points continuously decrease as they extend further back in time.- the equation actually used to calculate the forecast is convenient for programming on the computer since it requires as data only the actual and forecast values from the previous time point.- we need a formal process and criteria for choosing the “best” smoothing constant.CONTOH

25Exponential Smoothing ExampleIF  = and The first period forecast was Period Actual6 2057 1808 1829 ?Find the forecast for the 9th Period.This slide begins an exponential smoothing example.

34Exponential SmoothingFt = Ft (At-1 - Ft-1)Forecast,FPeriodtActual(α= .10)1180(Given)2168( ) =3159( ) =This slide illustrates the result of the steps used to make the forecast desired in the example. In the PowerPoint presentation, there are additional slides to illustrate the individual steps.4175( ) =5190( ) =6205( ) =

35Exponential SmoothingFt = Ft (At-1 - Ft-1)Forecast,FPeriodtActual(α= .10)4175( ) =5190( ) =6205( ) =This slide illustrates the result of the steps used to make the forecast desired in the example. In the PowerPoint presentation, there are additional slides to illustrate the individual steps.7180( ) =89

36Exponential SmoothingFt = Ft (At-1 - Ft-1)Forecast,FtPeriodActual(α= .10)4175( ) =5190( ) =6205( ) =7This slide illustrates the result of the steps used to make the forecast desired in the example. In the PowerPoint presentation, there are additional slides to illustrate the individual steps.180( ) =8182( ) =?( ) =9

42Forecast Error EquationsMean Square Error (MSE)Mean Absolute Deviation (MAD)Mean Absolute Percent Error (MAPE)This slide illustrates the equations for two measures of forecast error. Students might be asked if there is an occasion when one method might be preferred over the other.

43Selecting Forecasting Model ExampleHow to calculate the accuracy of forecast?ExampleActual ExponentialSmoothing Year Sales Forecast (.9)This slide begins an example of choosing a model.

45Exponential Smoothing Methode EvaluationExponential Smoothing Model:MSE = Σ Error2 / n = / 5 =MAD = Σ |Error| / n = / 5 =MAPE = 100 Σ |Absolute percent errors|/n = 0.10/5 = 0.02This slide presents the result of the calculations of MSE and MAD for the Linear and Exponential Smoothing models.Students should be asked to choose the “better” model.Students should also be asked to consider the differences between the values calculated for the error measures for a given model, and between the two models. Do these differences tell us more than simply that one model is preferable to the other? (For example, is the exponential smoothing model 22 times better than the linear model?)

60Tracking Signal ComputationNoForcActErrorRSFEAbsCumMADTS1100902953115451256140-101010.0-1-5-15157.5-2|Error|TS = RSFE/MAD = -15/7.5 = -2This slide illustrates the last step in the calculation of a tracking signal for a simple example problem. The PowerPoint slide presentation contains this as the last of a sequence of slides - the others stepping through the actual calculation process.

61Plot of a Tracking SignalSignal exceeded limitTracking signalUpper control limit+MADAcceptable range-This slide illustrates a graph of a tracking signal form a “practical” problem.Lower control limitTime